If P != NP and the universe has no source of exponential computing power, then there are evidential updates too difficult for even a superintelligence to compute
What a strange thing for my past self to say. This has nothing to do with P!=NP and I really feel like I knew enough math to know that in 2008; and I don’t remember saying this or what I was thinking.
To execute an exact update on the evidence, you’ve got to be able to figure out the likelihood of that evidence given every hypothesis; if you allow all computable Cartesian environments as possible explanations, exact updates aren’t computable. All exact updates take place inside restricted hypothesis classes and they’ve often got to be pretty restrictive. Even if every individual hypothesis fits inside your computer, the whole set probably won’t.
What a strange thing for my past self to say. This has nothing to do with P!=NP and I really feel like I knew enough math to know that in 2008; and I don’t remember saying this or what I was thinking.
To execute an exact update on the evidence, you’ve got to be able to figure out the likelihood of that evidence given every hypothesis; if you allow all computable Cartesian environments as possible explanations, exact updates aren’t computable. All exact updates take place inside restricted hypothesis classes and they’ve often got to be pretty restrictive. Even if every individual hypothesis fits inside your computer, the whole set probably won’t.